How to Calculate the Current Stock Price of Jia's Fashions

What is the method to determine the current stock price of Jia's Fashions based on the provided information?

How much should Jia's Fashions common stock sell for today if her required return is 10.5%?

Answer:

The current stock price of Jia's Fashions should be $59.16.

Explanation:

To calculate the current stock price of Jia’s Fashions, we need to project the future dividends based on the growth percentages provided and discount them back to present value using the required rate of return. The calculation involves projecting dividend growth for the upcoming years and then determining the present value of these dividends. Additionally, we need to factor in a perpetuity of dividends starting from the fourth year onwards, which represents an indefinite period of dividend payments.

The stock price is determined by utilizing a discounted cash flow model, which considers the future dividends of the company and discounts them back to their present value using the required rate of return. The provided information states that the dividends of Jia's Fashions will increase by different percentages over the following years and these future dividends should be discounted at the required return rate of 10.5%.

Projection of Jia's Fashions dividends:

Year 1: $2.00 × 1.20 = $2.40

Year 2: $2.40 × 1.12 = $2.688

Year 3: $2.688 × 1.12 = $3.01056

From Year 4 onwards, dividends will grow at 6% indefinitely.

The calculation includes:

1. Present value of dividends for the first three years

2. Present value of the perpetuity of dividends from Year 4 onwards

Adding these two components gives the current stock price:

PV (Years 1-3 dividends) = $2.40 / (1+0.105) + $2.688 / (1+0.105)² + $3.01056 / (1+0.105)³

PV (dividends from Year 4 onwards) = $3.01056 × (1+0.06) / [(0.105-0.06) × (1.105³)]